The major
use of matrices is to indicate cause and effect by listing
activities along the horizontal axis and environmental parameters
along the vertical axis. In this way the impacts of both
individual components of projects as well as major alternatives
can be compared. The simplest matrices use a single mark to show
whether an impact is predicted or not. However it is easy to
increase the information level by changing the size of the mark
to indicate scale, or by using a variety of symbols to indicate
different attributes of the impact. An example of a matrix is
given as Table 2. The choice of symbols in this example enables
the reader to see at a glance whether or not there was an impact
and, if so, whether the impact was beneficial or detrimental,
temporary or permanent. Figure 8 is another example of a matrix,
in this case used to clearly indicate the importance of a range
of wetland values.

ICOLD has
prepared a large and comprehensive matrix for use in EIAs for
dams. The system of symbols for each box shows: whether the
impact is beneficial or detrimental; the scale of the impact; the
probability of occurrence; the time-scale of occurrence; and,
whether the design has taken the impact into account, (ICOLD,
1980). This comprehensive approach, however, makes the final
output rather difficult to use and a maximum of three criteria is
recommended per impact to maintain clarity. Ahmad and Sammy
(1985) suggest that the most important criteria are: magnitude,
or degree of change; geographical extent; significance; and,
special sensitivity. "Significance" could be further
sub-divided to indicate why an impact is significant. For
example, it may be because of irreversibility, economic
vulnerability, a threat to rare species etc. "Special
sensitivity" refers to locally important issues. A series of
matrices at all stages of the EIA process can be a particularly
effective way of presenting information. Each matrix may be used
to compare options rated against a few criteria at a time.

The
greatest drawback of matrices are that they can only effectively
illustrate primary impacts. Network diagrams, described
below, are a useful and complementary form of illustration to
matrices as their main purpose is to illustrate higher order
impacts and to indicate how impacts are inter-related.

Matrices
help to choose between alternatives by consensus. One method is
to make pair-wise comparisons. It provides a simple way for a
group of people to compare a large number of options and reduce
them to a few choices. First a matrix is drawn with all options
listed both horizontally and vertically. Each option is then
compared with every other one and a score of 1 assigned to the
preferred option or 0.5 to both options if no preference is
agreed.

An example
of such a matrix is given as Table 3. As can be seen, Z is the
preferred option.

A number of
methods have been developed to compare impacts by applying values
to them. The relative importance of impacts, eg wetlands loss
versus rare species loss, or the relative importance of criteria,
e.g. economic vulnerability versus probability of occurrence,
will depend on the local environment and priorities. Ranking, and
therefore implicitly value, can be determined by using the
pair-wise comparison technique described above, except that,
rather than comparing options, criteria are compared instead.
This can enable a series of weightings to be developed which will
be entirely site-specific and dependent upon the subjective
choices of those participating in the group which develops the
weightings.

TABLE 3:
Example of pair-wise comparison

Compare alternative

With alternative

Sum

W

X

Y

Z

W

-

0

0

0.5

0.5

X

1

-

1

0

2

Y

1

0

-

0

1

Z

0.5

1

1

-

2.5

A simple
example would be to develop weightings for environmental versus
economic acceptability. Thus, in the example illustrated in
Figure 2, weightings would have to be developed to determine the
preference for either option B or option C. Is more weight to be
given to environmental or economic criteria?

Reducing
information about impacts to a single number should be avoided as
it obscures understanding and disguises the subjective nature of
the analysis. However, it can be useful to compare, for example,
the degree to which different mitigating options are effective in
managing water quality.